Economic and financial modeling and planning is commonly used to estimate or predict the performance and outcome of real systems given specific sets of input data of interest. A model is a mathematical expression or representation which predicts the outcome or behavior of the system under a variety of conditions. In one sense, it is relatively easy to review historical data, understand its past performance, and state with relative certainty that the system's past behavior was indeed driven by the historical data. A much more difficult task, but one that is extremely valuable, is to generate a mathematical model of the system which predicts how the system will behave, or would have behaved, with different sets of data and assumptions. While forecasting and backcasting using different sets of input data is inherently imprecise, i.e., no model can achieve 100% certainty. The field of probability and statistics has provided many tools which allow such predictions to be made with reasonable certainty and acceptable levels of confidence.
In its basic form, the economic model can be viewed as a predicted or anticipated outcome of a mathematical expression as driven by a given set of input data and assumptions. The input data is processed through the mathematical expression representing either the expected or current behavior of the real system. The mathematical expression is formulated or derived from principles of probability and statistics, often by analyzing historical data and corresponding known outcomes, to achieve a best fit of the expected behavior of the system to other sets of data, both in terms of forecasting and backcasting. In other words, the model should be able to predict the outcome or response of the system to a specific set of data being considered or proposed, within a level of confidence, or an acceptable level of uncertainty. As a simple test of the quality of the model, if historical data is processed through the model and the outcome of the model, using the historical data, is closely aligned with the known historical outcome, then the model is considered to have a high confidence level over the interval. The model should then do a good job of predicting outcomes of the system to different sets of input data.
The process of setting the interest rates or prices for retail bank deposit and loan accounts is an essential task in a financial services institution. Recently, large financial institutions have started using sophisticated analytics and modeling to understand demand trends and uncover areas of profit opportunity. Automated pricing software represents a movement toward greater precision in the pricing process. The new technology relies on complex demand models to estimate customers' attitudes toward price and the elasticity of demand from historical sales data.
One of the most difficult problems in demand modeling is the existence of products that have little or no historical data available. A similar problem is when there are no price changes in the sales history of a product, or if a price does change it is associated with a promotion, a competitor price move, or a cost change. In the latter case, there is little information about the effect of pure price changes on consumer demand. This lack of information makes traditional regression analysis very unstable and can result in a large number of incorrect price elasticities.
One possible solution to this problem is a statistical method called Bayesian inference. Bayesian inference is a method of determining stable and robust estimates of parameters by taking into consideration the learning from prior distributions of the corresponding parameter estimates. Generally speaking, Bayesian inference methods require the knowledge of a-priori guesses for the model parameters. Such guesses define what is known about the model parameters prior to observing the data used for modeling. During the modeling process, these guesses are then used in a way similar to “attractor points” for the parameters estimated by demand models, thus stabilizing the modeling process. Such methods can be thought of as a mathematical approach to mixing facts (the data) with educated guesses (the priors). The quality of such Bayesian priors is very important for the quality of the final estimates of model parameters.
Stability is one of the main advantages of Bayesian modeling methods. In the total absence of information (i.e., zero statistical content of the data), the model parameters will reproduce exactly the Bayesian priors. In the ideal case, where there is an infinite amount of data with infinite information content, the value of the Bayesian priors has no effect on the final value of the model parameters. In practice, the data is noisy with limited statistical information in it. For such cases the value of the model parameters will reflect a trade off between the statistical content of the data and the Bayesian priors, hence the quality of such priors is extremely important for the quality of the resulting model.
There are some existing techniques of determining Bayesian priors. One classic technique is to use expert opinion for the value of priors. The expert opinion may be obtained from professionals in the field who have studied some aspect of the modeling objects in question. Another technique uses aggregated values from a related, larger data set to determine the priors.
However, these traditional techniques may not be feasible or efficient in determining Bayesian priors for price elasticity in a retail banking environment where one would like to systematically, automatically and quickly obtain the priors for a large number of products. In some cases, the expert option is too expensive to obtain or simply not available in time for thousands of financial products. In other cases, even the related data set is difficult to find, for example, when a new product line is introduced and hence no historical data can be used as reference.
There is a need for a method of determining Bayesian priors for price elasticity that is efficient, economical, and reliable.